Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria

arXiv:2610.01356v1 Announce Type: new Abstract: Stable port-Hamiltonian neural networks certify asymptotic stability by construction. Yet, their Hamiltonian is a global Lyapunov function with a single global minimum, so they can represent only dynamic systems with {one} attractor. We demonstrate that this excludes even simple systems with energy landscapes forming a double well, and we overcome the restriction by parametrising the Hamiltonian as a {product} of Bregman divergences generated by one input-convex network. We prove that the resulting model is locally Lyapunov stable, that the coexistence of stable equilibria forces additional non-asymptotically-stable equilibria to exist, that all equilibria lie in a bounded region, and under a hyperbolicity assumption that almost-everywhere stability holds. On three systems our approach is able to recover the energy surface characteristics and improve the convergence speed by 1.8imes-8.5imes.

Related

• Learning Lyapunov Operators for Nonlinear Systems
• Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics
• Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks
• Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems

Source: arXiv cs.LG | 2026-10-02